Помогите пожалуйста с логарифмами с подробным решением. Даю 15 баллов.Вычислить: [tex]

log(5) = 1 / log(150)

log(30) : (1 / log(150)) = log(30) * log(150) = log(5*6) * log(6*25) =

= ( log(5)+log(6) ) * ( log(25)+log(6) ) = ( 1+log(6) ) * ( 2+log(6) )

подобно:

log(750) : (1 / log(6)) = log(750) * log(6) = log(6*125) * log(6) =

= ( log(125)+log(6) ) * log(6) = ( 3+log(6) ) * log(6)

осталось вычесть... комфортно обозначить x = log(6)

( 1+x ) * ( 2+x ) - ( 3+x ) * x = 2+x+2x+x - 3x-x = 2

------------------------------------------------------------------------

log(70) : (1 / log(280)) = log(70) * log(280) = log(35*2) * log(35*8) =

= ( log(2)+log(35) ) * ( log(8)+log(35) ) = ( 1+log(35) ) * ( 3+log(35) )

аналогично:

log(560) : (1 / log(35)) = log(560) * log(35) = log(16*35) * log(35) =

= ( log(16)+log(35) ) * log(35) = ( 4+log(35) ) * log(35)

осталось вычесть... удобно обозначить x = log(35)

( 1+x ) * ( 3+x ) - ( 4+x ) * x = 3+x+3x+x - 4x-x = 3